= 6 that lies in the first oct riented upward.

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5. Let F = -9zi+ (xe"² – 2xe²²)+ 12 k. Find ſg F .dø and let S be the portion
of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (see
figure to the right), oriented upward.
(a) Explain why the formula F Ã cannot be used to find the flux of F through the surface S. Please be
specific and use a complete sentence.
Transcribed Image Text:5. Let F = -9zi+ (xe"² – 2xe²²)+ 12 k. Find ſg F .dø and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (see figure to the right), oriented upward. (a) Explain why the formula F à cannot be used to find the flux of F through the surface S. Please be specific and use a complete sentence.
Expert Solution
Step 1

Given:

F=-9zi+xexz-2xex2j+12k

The equation of the plain given is 2x+3z=6

Step 2

Since "S" is closed so divergence of "F" is given as follows,

Flux =div F dv

 

On applying the given equation in the above divergence,

di VF=x-9z+yxexz-2xex2+z12

di VF = 0+0+0=0

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